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arXiv:1906.05292 · Physical review. B./Physical review. B

Quantum many-body scars in a Landau level on a thin torus

Sanjay Moudgalya, Bogdan Andrei Bernevig, Nicolas Regnault

Published Nov 30, 2020• 89 citations
arXivHTMLPDF

Abstract

We study a kinetically constrained pair-hopping model that arises within a Landau level in the quantum Hall effect. At filling $\ensuremath{\nu}=1/3$, the model exactly maps onto the so-called ``PXP model,'' a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors $\ensuremath{\nu}=p/(2p+1)$, and show that the model is equivalent to nonintegrable spin chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.

DOI
10.1103/physrevb.102.195150

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We study a kinetically constrained pair-hopping model that arises within a Landau level in the quantum Hall effect. At filling \ensuremathν=1/3\ensuremath{\nu}=1/3\ensuremathν=1/3, the model exactly maps onto the so-called ``PXP model,'' a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors \ensuremathν=p/(2p+1)\ensuremath{\nu}=p/(2p+1)\ensuremathν=p/(2p+1), and show that the model is equivalent to nonintegrable spin chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.
Experimental observation of coherent oscillations in a Rydberg atom chain [H. Bernien et al., Nature (London) 551, 579 (2017)] has led to the discovery of quantum many-body scars (QMBSs) which is a new paradigm for ergodicity breaking. The experimental findings in the Rydberg chain can be well captured by a kinetically constrained model called the ``PXP'' model, which has been shown to host the eigenstate thermalization hypothesis (ETH)-violating scar states in the middle of the spectrum. Much effort has been put into identifying similar kinetically restricted systems that show a violation of ETH. In this paper, we study the QMBSs that can arise in one such model, namely the spin-1 Kitaev chain, where owing to some conserved quantities, the Hilbert space gets fragmented into unequal disconnected subspaces. Recently, You et al. [Phys. Rev. Res. 4, 013103 (2022)] showed that the ground state sector of this chain can be mapped exactly onto the prototypical PXP model and thus hosts QMBSs. Here, we demonstrate that the phenomenon of scarring is also present in other sectors, and in particular, we identify a sector that exhibits substantially more scarring than the ground state one. We propose an initial state and numerically demonstrate that its fidelity revivals are pronounced and longer lived than those in the PXP model.
We demonstrate that the kinematically constrained model of Rydberg atoms on a two-leg ladder with staggered detuning, $\mathrm{\ensuremath{\Delta}}\ensuremath{\in}[0,1]$, has quantum many-body scars (QMBSs) in its spectrum and represents a nonperturbative generalization of the paradigmatic PXP model defined on a chain. We show that these QMBSs result in coherent many-body revivals and site-dependent magnetization dynamics for both N\'eel and Rydberg vacuum initial states around $\mathrm{\ensuremath{\Delta}}=1$. The latter feature leads to eigenstate thermalization hypothesis (ETH)-violating finite imbalance at long times in a disorder-free system. This is further demonstrated by constructing appropriate local imbalance operators that display nonzero long-time averages for N\'eel and vacuum initial states. We also study the fidelity and Shannon entropy for such dynamics which, along with the presence of long-time finite imbalance, brings out the qualitatively different nature of QMBSs in PXP ladders with $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}1$ from those in the PXP chain. Finally, we identify additional exact midspectrum zero modes that stay unchanged as a function of $\mathrm{\ensuremath{\Delta}}$ and violate ETH.
Abstract We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential. Surprisingly in a strong resonance regime, we show that the model can be described by the kinetically constrained effective Hamiltonian, and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization, which are composed of two distinct sets of constrained nearest-neighbor hopping terms: one set acting exclusively on odd bonds and the other on even bonds. Specifically it is shown that each part can be independently mapped onto the well-known PXP model, therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model. As a consequence, we numerically demonstrate this system can host the so-called quantum many-body scars, which present dynamical revivals and ergodicity-breaking behaviors. However in sharp contrast with traditional quantum many-body scars, here the scarring states in our model driven by different parts of Hamiltonian will revive in different periods, and those of double parts can display a biperiodic revival pattern, both originating from the Hamiltonian dimerization. Besides, the condition of off-resonance is also discussed and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics. Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.
Persistent revivals recently observed in Rydberg atom simulators have challenged our understanding of thermalization and attracted much interest to the concept of quantum many-body scars (QMBSs). QMBSs are non-thermal highly excited eigenstates that coexist with typical eigenstates in the spectrum of many-body Hamiltonians, and have since been reported in multiple theoretical models, including the so-called PXP model, approximately realized by Rydberg simulators. At the same time, questions of how common QMBSs are and in what models they are physically realized remain open. In this Letter, we demonstrate that QMBSs exist in a broader family of models that includes and generalizes PXP to longer-range constraints and states with different periodicity. We show that in each model, multiple QMBS families can be found. Each of them relies on a different approximate su(2) algebra, leading to oscillatory dynamics in all cases. However, in contrast to the PXP model, their observation requires launching dynamics from weakly entangled initial states rather than from a product state. QMBSs reported here may be experimentally probed using Rydberg atom simulator in the regime of longer-range Rydberg blockades.
To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $|{\mathbb{Z}}_{k}\ensuremath{\rangle}$ (k=2,3k=2,3k=2,3) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev-Heisenberg model using the density-matrix renormalization group and Lanczos exact diagonalization methods, and determine the phase diagram. We parametrize the two terms in the Hamiltonian by the angle $\ensuremath{\phi}$, where the Kitaev term is $K\ensuremath{\equiv}sin(\ensuremath{\phi})$ and competes with the Heisenberg $J\ensuremath{\equiv}cos(\ensuremath{\phi})$ term. One finds a rich ground-state phase diagram as a function of the angle $\ensuremath{\phi}$. Depending on the ratio $K/J\ensuremath{\equiv}tan(\ensuremath{\phi})$, the system either breaks the symmetry to one of distinct symmetry broken phases, or preserves the symmetry in a quantum spin-liquid phase with frustrated interactions. We find that the scarred state is stable for perturbations which obey Z2{\mathbb{Z}}_{2}Z2​-symmetry, while it becomes unstable against Heisenberg-type perturbations.
We discover a variety of exact quantum many-body scars in higher-spin kinetically constrained models through the recently developed DMRG-S algorithm [Zhang et al., Phys. Rev. Lett. 131, 020402 (2023)]. Specifically, for the higher-spin PXP model on arbitrary bipartite lattices of any spatial dimension, we find exact many-body scars that are equidistantly spaced in the energy spectrum and exhibit similar structures to the ground state of the Affleck-Kennedy-Lieb-Tasaki model. For the one-dimensional Fermi-Hubbard model with a tilted potential in a certain parameter regime, whose effective model is equivalent to a kinetically constrained spin model with four degrees of freedom on each site, we find several many-body scars at energy E=0E=0E=0 and $E=\ifmmode\pm\else\textpm\fi{}\sqrt{2}$ that can be exactly represented as matrix product states with finite bond dimensions. Our results demonstrate that larger local degrees of freedom in the kinetically constrained models provide a much broader space for the emergence of quantum many-body scars and weak ergodicity breaking.